On some approximations in applications of <i>X</i>α theory

Dunlap, Brett I.; Connolly, John; Sabin, John R.

doi:10.1063/1.438728

Cited by 1,444 publications

(778 citation statements)

References 29 publications

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“…However, these algorithms currently only work efficiently for large systems in very small basis sets. When more accuracy is needed larger basis sets are essential and for these cases the resolution of identity (RI) method [1][2][3][4][5][6][7][8] has been used to reduce the computational effort. The RI method has worked very well for the calculation of the Coulomb contribution to the Fock matrix [9][10][11][12][13][14][15][16][17][18], but the exchange contribution is much more difficult to compute with the same benefits [15; 19-22].…”

Section: Introductionmentioning

confidence: 99%

Cholesky Decomposition Techniques in Electronic Structure Theory

Aquilante

Boman

Boström

et al. 2011

Challenges and Advances in Computational Chemistry and Physics

114

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We review recently developed methods to efficiently utilize the Cholesky decomposition technique in electronic structure calculations. The review starts with a brief introduction to the basics of the Cholesky decomposition technique. Subsequently, examples of applications of the technique to ab inito procedures are presented. The technique is demonstrated to be a special type of a resolution-of-identity or density-fitting scheme. This is followed by explicit examples of the Cholesky techniques used in orbital localization, computation of the exchange contribution to the Fock matrix, in MP2, gradient calculations, and so-called method specific

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Section: Introductionmentioning

confidence: 99%

Cholesky Decomposition Techniques in Electronic Structure Theory

Aquilante

Boman

Boström

et al. 2011

Challenges and Advances in Computational Chemistry and Physics

114

View full text Add to dashboard Cite

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“…The calculation of the MP2 energy within the RI-GPW 52 approach (RI-MP2) is closely related to the original GPW method. Here, the dual representation 5 of the electronic density is applied to the fitting density arising from the resolution of identity approximation [61][62][63] , where the RI fitting densities are obtained by introducing an auxiliary Gaussian basis and employing the Coulomb metric. 64 The model system consists of 64 water molecules in a cubic simulation cell under periodic boundary conditions (PBC).…”

mentioning

confidence: 99%

Bulk Liquid Water at Ambient Temperature and Pressure from MP2 Theory

Ben

Schönherr

Hutter

et al. 2013

J. Phys. Chem. Lett.

137

112

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MP2 provides a good description of hydrogen bonding in water clusters and includes longrange dispersion interactions without the need to introduce empirical elements in the description of the interatomic potential. To assess its performance for bulk liquid water under ambient conditions, an isobaric-isothermal (NpT) Monte Carlo simulation at the second-order Moller-Plesset perturbation theory level (MP2) has been performed. The obtained value of the water density is excellent (1.02 g/mL), and the calculated radial distribution functions are in fair agreement with experimental data. The MP2 results are compared to a few density functional approximations, including semilocal functionals, hybrid functionals, and functionals including empirical dispersion corrections. These results demonstrate the feasibility of directly sampling the potential energy surface of condensed-phase systems using correlated wave function theory, and their quality paves the way for further applications. Understanding the structural and electronic properties of liquid water at ambient conditions is a major challenge in condensed matter simulations. Water is a crucial ingredient for a large variety of systems of prime importance in basic chemistry, biology, and physics, as well as in the applied fields of catalysis and energy production. The water molecule has a large dipole moment and polarizability, is a multiple hydrogen donor and acceptor and can easily build network structures.The total cohesive energy in the condensed phase is, as a consequence of these properties, a sum of many weak interactions. Theoretical models face therefore the challenge to describe many different effects and their subtle interplay at a high precision. The development of sophisticated empirical potentials for water 1-10 , allowed to gain insights into water's behavior and its thermodynamic properties [11][12][13] , such as, density maxima, heat capacity and effects of supercooling. However, empirical models lack transferability and might fail if used under conditions away from their fitting range. Most importantly, as soon as water takes an active role in a chemical process, either as a strongly interacting solvent, or for example as a source of protons, the electronic properties of the water molecule need to be taken into account. In this respect, first-principles methods offer the possibility to describe all the underlying physics on the same footing, simplifying the treatment of intra-and inter-molecular interactions. The capability to reproduce properties of complex systems such as liquid water can therefore be used to judge the sophistication and predictive power of a given quantum mechanical model. Density functional theory (DFT) is the most used quantum mechanical method employed for studying physical and chemical properties of condensed phase systems. Many DFT based simulation of bulk water have been reported in the literature, and in this context three main methods of sampling the phase space can be recognized 14 : the Car-Parrinello molecula...

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“…To facilitate the efficient calculation of g for the MOs in polyatomic molecules, the integrals in the Appendix must be generalized to the multicenter case. In large systems, straightforward evaluation of the hFjjFji integral becomes computationally costly, but techniques based on the resolution of the identity (RI) [15][16][17] or resolution of the Coulomb operator [18][19][20] should be helpful in this context.…”

Section: Discussionmentioning

confidence: 99%

Diagnostics of molecular orbital quality

2010

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Abstract:We discuss several measures of the quality of a molecular orbital. Each requires only that the orbital be associated with a well-defined Fock operator and is thus applicable to both Hartree-Fock and density functional orbitals. One of the measures, the g diagnostic, ranges from g = 0 (perfect) to g = p/2 (poor) and is conceptually simple. We illustrate its usefulness by applying it to a number of small atoms and ions.Key words: molecular orbital quality, density functional theory, Hartree-Fock.Résumé : On discute de plusieurs mesures de la qualité d'une orbitale moléculaire. Chacune nécessite uniquement que l'orbitale soit associée à un opérateur de Fock bien défini et qu'il soit ainsi applicable aux orbitales de Hartree-Fock ainsi qu'aux fonctionnelles de densité. L'une ce ces mesures, le diagnostic, s'étend de 0 (parfait) à 2 (mauvais) et elle est conceptuellement simple. On illustre son utilité en l'appliquant à un certain nombre de petits atomes et de petits ions.Mots-clés : qualité d'une orbitale moléculaire, théorie de la fonctionnelle de la densité, Hartree-Fock.[Traduit par la Rédaction]

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On some approximations in applications of Xα theory

Cited by 1,444 publications

References 29 publications

Cholesky Decomposition Techniques in Electronic Structure Theory

Cholesky Decomposition Techniques in Electronic Structure Theory

Bulk Liquid Water at Ambient Temperature and Pressure from MP2 Theory

Diagnostics of molecular orbital quality

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